Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

Civil Engineering (CE) : Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

The document Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev is a part of Civil Engineering (CE) category.
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)

Torsion, Shear, and Flexure
→ Torsion
o Stress distribution on a cross section subject to torsion
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
Maximum shear stress, τmax 
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
where η = shape factor, T = torque, x , y = dimensions of the cross section. The shape factor is different for linear and nonlinear cases.

→ Failure mode
o Torsion failure of plain concrete occurs suddenly with an inclined tension crack in one of the wider faces, then extending into the narrow faces. Concrete crushing occurs in the opposite wider face.

→ Torsional strength, Tup, of plain concrete
o Several theories have been presented for computing torsional strength of plain concrete including elastic, plastic, and skew bending theories.
o Skew bending:
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

T is the applied torque and M, Ttw, are the bending and twisting moments, respectively, on the  Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev plane.

Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

where Tup= ultimate torsion for plain concrete when  σ reaches σ 
 Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

� Torsional strength contributed by steel
o Consider the system consisting of longitudinal and transverse (stirrups) steel:
( x1 , yare the dimensions of steel frame as shown.) 
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
o Torsional moment with respect to axis of the horizontal stirrups
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
where At= area of one stirrup leg,
fs = stirrup stress, and
s = stirrup spacing.

o Torsional moment with respect to axis of the horizontal stirrups
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
o Total torsional moment
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev  (αt is determined from experiment.)

� Design concept
o Total ultimate torsion capacity, T
T= Tc +Ts
where Tc = torsional capacity contributed by concrete, and
Ts = torsional capacity contributed by reinforcement.
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

The coefficient β represents reduction in torsional strength provided by concrete after cracking. Upon cracking of concrete stress and strain are partially transferred to steel. Stiffness and strength of the system will depend on the amount of transverse and longitudinal reinforcements.

o The final failure may be in one of the following ways:
1. Under reinforced → Both transverse and longitudinal steel yield before failure.
2. Over reinforced → Concrete crushes before yielding of steel.
3. Partially over (under) reinforced

o For under reinforced elements, αt is independent of the steel ratio.
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

o Code suggestion:
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

Role of longitudinal steel
1. It anchors the stirrups, particularly at corners.
2. It provides dowel resistance.
3. It controls crack widening.

� Condition of under reinforcement
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

where A= volume per length of longitudinal steel.
→ Steel yields first.

�Torsion combined with flexure

�Torsion combined with shear o Generally shear exists simultaneously with bending.
→ The existence of shear will reduce the resisting ability in torsion. Thus, it is necessary to consider the case of torsion combined with shear.

o For RC beams with transverse reinforcement:
→  Pure torsion: T= Tc +Ts
→ Pure shear:Vu = V+ Vs
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

� ACI Code o Design for torsion
→ Same interaction as in members without transverse reinforcement.

o Excess torque
→ Over and above that resisted by concrete, the same amount of reinforcement is provided in members subject to torsion plus shear as would be required for purely torsional members.
→ This torsional reinforcement is added to that required for carrying bending moments and flexural shears.

o Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
where T= factored torque,
φ = capacity reduction factor for torsion = 0.75,
Tn = nominal strength for torsion,
Tc = torsional moment carried by concrete, and
Ts = torsional moment carried by steel.

o Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

where Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev  pure torsion and Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev pure shear.

Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

]o Assume Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev such that

Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

o T≤ 4Tc is required to assure yielding of steel first.
o Minimum spacing of torsional stirrups → 4( x1 + y1 ) or 12 in.

� Condition of neglecting torsional effects
o Torsional effects may be neglected if
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

where   Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev sum of the small rectangles for irregular shapes.

� Hollow sections
Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev

o When Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev , consider the cross section as solid.
o When Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev assume it as solid but multiply   Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev
o When Torsion, Shear, and Flexure Civil Engineering (CE) Notes | EduRev consider it as a thin-walled section. → Check for instability (local buckling).

→ General formulation of post-cracking behavior of flexure, shear, and tension interaction in R/C beams
→  Discussion of applications: Concrete guideway systems from monorail and maglev transportation infrastructure.
→  Design Example – Shear and torsion

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

Free

,

practice quizzes

,

Objective type Questions

,

Viva Questions

,

Extra Questions

,

past year papers

,

Shear

,

Sample Paper

,

Summary

,

MCQs

,

Exam

,

mock tests for examination

,

Important questions

,

video lectures

,

Previous Year Questions with Solutions

,

shortcuts and tricks

,

Semester Notes

,

study material

,

and Flexure Civil Engineering (CE) Notes | EduRev

,

Shear

,

and Flexure Civil Engineering (CE) Notes | EduRev

,

Torsion

,

pdf

,

and Flexure Civil Engineering (CE) Notes | EduRev

,

Shear

,

Torsion

,

ppt

,

Torsion

;